The sector of a circular plate shown in the figure has its center of mass at $y_{CM} =$

$A$ sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass is at the maximum distance from the original centre. What is this distance?

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The centre of the hole is at the centre of the square. The centre of mass of the remaining part is:

$A$ uniform thin metal plate of mass $10 \ kg$ with the dimensions shown in the figure is given. The ratio of the $x$ and $y$ coordinates of the center of mass of the plate is $\frac{n}{9}$. The value of $n$ is:

$A$ carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of the cone,the position of the centre of mass of the toy is given by

$A$ uniform square plate is shown in the figure. Four identical small squares are removed from its corners. Where will the $C.M.$ (Center of Mass) be located after removing all four squares? Give the answer in terms of quadrants and axes.